Some Complexity Results on Inconsistency Measurement

We survey a selection of inconsistency measures from the literature and investigate their computational complexity wrt. decision problems related to bounds on the inconsistency value and the functional problem of determining the actual value. Our findings show that those inconsistency measures can be partitioned into three classes related to their complexity. The first class contains measures whose complexity are located on the first level of the polynomial hierarchy, the second class contains measures on the second level of the polynomial hierarchy, and the third class is located beyond the second level of the polynomial hierarchy. We provide membership results for all the investigated problems and completeness results for most of them.